Skip to main content
SpringerLink
Log in

Mackey, Harish-Chandra, and representation theory

  • Chapter
  • First Online:
Reflections on Quanta, Symmetries, and Supersymmetries

  • 1366 Accesses

Abstract

Some personal reminiscences of Mackey and Harish-Chandra together with brief comments on their work.

Over the years I have spoken on many occasions on the work of George Mackey and Harish-Chandra on representation theory, and what it has meant to me. This essay draws upon my articles as well as of my memories.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R. S. Doran, C. C. Moore, and R. S. Zimmer, (Eds.), George Mackey and his work on representation theory and foundations of physics. Group representations, ergodic theory, and mathematical physics: a tribute to George W. Mackey, 417446, Contemp. Math., 449, Amer. Math. Soc., Providence, RI, 2008.

    Google Scholar 

  2. R. S. Doran, and A. Ramsay,George Mackey 1916–2006, Notices of the Amer. math. Soc., 54(2007), 824–850.

    MathSciNet  MATH  Google Scholar 

  3. C. Carmeli, G. Cassinelli, A. Toigo, and V. S. Varadarajan, Unitary representations of super Lie groups and applications to the classification and multiplet structure of super particles, Comm. Math. Phys., 263(2006), 217–258.

    Article  MathSciNet  MATH  Google Scholar 

  4. H. Salmasian,Unitary representations of nilpotent super Lie groups, Comm. Math. Phys., 297(2010), 189–227.

    Article  MathSciNet  MATH  Google Scholar 

  5. C. C. Moore, Group extensions of p-adic and adelic linear groups, Pub. Math. IHES, 35(1968), 5–70.

    MATH  Google Scholar 

  6. R. J. Zimmer, Ergodic Theory and Semisimple Groups, Birkhäuser, 1984.

    Google Scholar 

  7. R. Howe, On a notion of rank for unitary representations of the classical groups, Harmonic analysis and grouprepresentations, 223–331, Liguori, Naples, 1982.

    Google Scholar 

  8. J,-S. Li, On the classification of irreducible low rank unitary representations of classical groups, Compositio Math. 71 (1989), no. 1, 29–48.

    Google Scholar 

  9. H. Salamsian, A notion of rank for unitary representations of reductive groups based on Kirillov’s orbit method. Duke Math. Jour. 136 (2007), 1–49.

    Google Scholar 

  10. V. S. Varadarajan, Some mathematical reminiscences, Methods Appl. Anal. 9 (2002) v-xviii.

    Google Scholar 

  11. V. S. Varadarajan, Harish-Chandra, HisWork, and its Legacy, in The Mathematical Legacy of Harish-Chandra, 1–35, R. S. Doran, and V. S. Varadarajan, (Eds.), Amer. Math. Soc., Proc. Symp. in Pure Math., Vol. 68, 2000.

    Google Scholar 

  12. P. C. Trombi, and V. S. Varadarajan,Spherical transforms of semisimple Lie groups, Ann. of Math. (2) 94(1971), 246–303.

    Article  MathSciNet  Google Scholar 

  13. P. C. Trombi, and V. S. Varadarajan, Asymptotic behaviour of eigen functions on a semisimple Lie group: the discrete spectrum, Acta. Math. 129 (1972), 237–280.

    Article  MathSciNet  MATH  Google Scholar 

  14. J. A. C. Kolk, and V. S. Varadarajan, On the transverse symbol of vectorial distributions and some applications to harmonic analysis, Indag. Math. (N.S.) 7 (1996), 67–96.

    Google Scholar 

  15. Harish-Chandra Collected Papers, Vol. IV., [1970c], Springer-Verlag, 1984.

    Google Scholar 

  16. Harish-Chandra Collected Papers, Vol. I., [1964a]-[1966b], Springer -Verlag, 1984.

    Google Scholar 

  17. Harish-Chandra Collected Papers, Vol. IV., [1973], Springer -Verlag, 1984.

    Google Scholar 

  18. Harish-Chandra Collected Papers, Vol. IV., [1977b] [1977b’], Springer -Verlag, 1984.

    Google Scholar 

  19. Harish-Chandra Collected Papers, Vol. III., [1963], Springer -Verlag, 1984.

    Google Scholar 

  20. Harish-Chandra Collected Papers, Vol. III., [1968a], Springer -Verlag, 1984.

    Google Scholar 

  21. Harish-Chandra, My association with Professor Dirac, in Reminiscences about a great physicist: Paul Adrien Maurice Dirac, 34–36, B. N. Kursunoglu, and E. P. Wigner, (Eds.), Cambridge Univ. Press, Cambridge, 1987.

    Google Scholar 

  22. The Mathematical Legacy of Harish-Chandra, R. S. Doran, and V. S. Varadarajan, (Eds.), Amer. Math. Soc., Proc. Symp. in Pure Math., Vol. 68, 2000.

    Google Scholar 

  23. Harish-Chandra Collected Papers, Vol. I., [1951f], Springer -Verlag, 1984.

    Google Scholar 

  24. Harish-Chandra Collected Papers, Vol. I., [1952], Springer -Verlag, 1984.

    Google Scholar 

  25. Harish-Chandra Collected Papers, Vol. I., [1954e], Springer -Verlag, 1984.

    Google Scholar 

  26. Harish-Chandra Collected Papers, Vol. I., [1956a], Springer -Verlag, 1984.

    Google Scholar 

  27. H. Weyl, Gesammelte Abhandlungen, Band I, 248–297. Springer-Verlag, 1968.

    Google Scholar 

  28. Harish-Chandra Collected Papers, Vol. I., [1958a] [1958b], Springer -Verlag, 1984.

    Google Scholar 

  29. Harish-Chandra Collected Papers, Vol. I., [1968b], Springer -Verlag, 1984.

    Google Scholar 

  30. Harish-Chandra Collected Papers, Vol. I., Springer -Verlag, 1984.

    Google Scholar 

  31. V. S. Varadarajan, Harmonic Analysis on Real Reductive Groups, Springer Lecture Notes in Mathematics No., 576, Springer-Verlag, 1977.

    Google Scholar 

  32. Lie Theory Harmonic Analysis on Symmetric Spaces - General Plancherel Theorems, J-P. Anker, B. Orsted (Eds.), Progress in Math. 230, Birkhauser, Boston, 2005. See in the same volume

    Google Scholar 

  33. E. P. Van den Ban, The Plancherel theorem for a reductive symmetric space, loc. cit., 1–97; see also http://www.math.uu.nl/people/ban/manus/banesgt.ps

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of California, 90095-1555, Los Angeles, CA, USA

    V. S. Varadarajan

Authors
  1. V. S. Varadarajan
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Varadarajan, V.S. (2011). Mackey, Harish-Chandra, and representation theory. In: Reflections on Quanta, Symmetries, and Supersymmetries. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-0667-0_8

Download citation

Publish with us

Policies and ethics

Search

Navigation